Re: [EM] The critical importance of Precinct Summability.
RP, Schulze, MiniMax needs N(N-1) tallies.Condorcet-Plurality or Condorcet-TTR needs N^2 tallies.Since cycles are rare and not predictable, I'm just not as worried as you scholars are about the differences in Condorcet methods regarding resistance to strategy.3 years ago I was plugging BTR-IRV because it was a simple modification to IRV, already in use. But since I have been convinced that the law should be a two-method Condorcet system. The law should say what it means and means what it says. In the most pedestrian language possible.Last year we introduced H.424 which was Condorcet-Plurality. Next year (new legislative session) I hope to persuade Bob and Carol to introduce another Condorcet RCV bill, this time maybe Condorcet-TTR which might be better, almost identical to Condorcet-IRV, but without all the round-by-round baggage.Powered by Cricket Wireless------ Original message------From: Kristofer Munsterhjelm Date: Thu, Aug 8, 2024 06:50To: robert bristow-johnson;election
-methods@lists.electorama.com;Cc: Subject:Re: [EM] The critical importance of Precinct Summability.On 2024-08-07 04:11, robert bristow-johnson wrote:
From: robert bristow-johnson
Sent: Tuesday, August 6, 2024 10:08 AM
To: Mike McCarthy ; Robert Hooper ; Carol Ode ; Abbey Duke ; Irene Wrenner ; Thomas Chittenden ; Sarah Copeland Hanzas
Subject: [External] The critical importance of Precinct Summability.
I agree. It's surprising that Venezuela has such a good reporting system
if the authorities want to rig the elections anyway, though!
It's also unfortunate that I haven't found any suitable summable analogs
of the resistant set for strategy resistance. I have some ideas of where
I should look, but nothing concrete has come of it. Maybe it will turn
out that the strongest manipulation resistance can only be achieved by
giving up summability. But perhaps it doesn't matter. Perhaps RP is good
enough :)
Thank you for letting the politicians know, in any case!
-km
On 2024-08-08 13:59, robert bristow-johnson wrote:
RP, Schulze, MiniMax needs N(N-1) tallies.
Condorcet-Plurality or Condorcet-TTR needs N^2 tallies.
Since cycles are rare and not predictable, I'm just not as worried as
you scholars are about the differences in Condorcet methods regarding
resistance to strategy.
That's a fair point.
3 years ago I was plugging BTR-IRV because it was a simple modification
to IRV, already in use. But since I have been convinced that the law
should be a two-method Condorcet system. The law should say what it
means and means what it says. In the most pedestrian language possible.
Last year we introduced H.424 which was Condorcet-Plurality. Next year
(new legislative session) I hope to persuad e Bob and Carol to introduce
another Condorcet RCV bill, this time maybe Condorcet-TTR which might be
better, almost identical to Condorcet-IRV, but without all the
round-by-round baggage.
What do you think of minmax? No round-by-round, just "whoever does best
one-on-one against his toughest rival". Too foreign for people used to
top count methods like Plurality and TTR?
Copeland,TTR would give you Smith. But it might be too complicated
(count number of pairwise wins per candidate, more is better, then if
there's a tie, choose the two tied candidates with most first
preferences and elect the one who beats the other pairwise).
-km
I suspect the uncovered set might be slightly better because it's a close
approximation of the bipartisan set that isn't too hard to explain. Maximal
lotteries also have some very nice strategy-resistance properties.
On this topic and the lack of focus on proportional representation
mentioned elsewhere, I think it would be super useful to have some kind of
strongly-summable PR algorithm. ElectoWiki claims Ebert's method is summable
https://electowiki.org/wiki/Summability_criterion#Multi-winner_generalizations_and_results,
but the link is broken and Ebert has some big issues (e.g. negative
response and Pareto inefficiency).
On Thu, Aug 8, 2024 at 7:04 AM Kristofer Munsterhjelm <
km-elmet@munsterhjelm.no> wrote:
On 2024-08-08 13:59, robert bristow-johnson wrote:
RP, Schulze, MiniMax needs N(N-1) tallies.
Condorcet-Plurality or Condorcet-TTR needs N^2 tallies.
Since cycles are rare and not predictable, I'm just not as worried as
you scholars are about the differences in Condorcet methods regarding
resistance to strategy.
That's a fair point.
3 years ago I was plugging BTR-IRV because it was a simple modification
to IRV, already in use. But since I have been convinced that the law
should be a two-method Condorcet system. The law should say what it
means and means what it says. In the most pedestrian language possible.
Last year we introduced H.424 which was Condorcet-Plurality. Next year
(new legislative session) I hope to persuad e Bob and Carol to introduce
another Condorcet RCV bill, this time maybe Condorcet-TTR which might be
better, almost identical to Condorcet-IRV, but without all the
round-by-round baggage.
What do you think of minmax? No round-by-round, just "whoever does best
one-on-one against his toughest rival". Too foreign for people used to
top count methods like Plurality and TTR?
Copeland,TTR would give you Smith. But it might be too complicated
(count number of pairwise wins per candidate, more is better, then if
there's a tie, choose the two tied candidates with most first
preferences and elect the one who beats the other pairwise).
-km
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info
On 2024-08-08 17:53, Closed Limelike Curves wrote:
I suspect the uncovered set might be slightly better because it's a
close approximation of the bipartisan set that isn't too hard to
explain. Maximal lotteries also have some very nice strategy-resistance
properties.
You've referred to the maximal lottery and strategic voting before. I'd
like to know in more detail what you're referring to by your statements.
In the Monroe post, you said:
If group strategy was a reasonable model of voters, it wouldn't
matter which electoral system we picked, because the outcome would
always be maximal lottery.
What do you mean? Do you mean that:
-
Every (non-strategyproof) method has a unique Nash equilibrium per
election under group strategy, whose expected outcome is that election's
maximal lottery, -
Every method has the maximal lottery as one of its Nash equilibria,
-
The relation between group strategy and the maximal lottery only holds
for some methods, and these methods have the ML as their unique Nash
equilibrium, -
As above, but "as one of its Nash equilibria".
or something else entirely?
On this topic and the lack of focus on proportional representation
mentioned elsewhere, I think it would be super useful to have some kind
of strongly-summable PR algorithm. ElectoWiki claims Ebert's method is
summable
https://electowiki.org/wiki/Summability_criterion#Multi-winner_generalizations_and_results, but the link is broken and Ebert has some big issues (e.g. negative response and Pareto inefficiency).
I tried to look at the forum through IA and I couldn't find any mention
of strong summability; it must have been in a later post on that thread,
which IA hasn't archived. So at best that needs a {{cn}}.
To my knowledge, whether Droop proportionality is compatible with strong
summability is still open. I have a very broad idea of how one might
resolve summability questions like this, but I would need some
mathematical primitives that I'm not sure how to construct.
-km
I think votingtheory.org has saved all the conversations from that forum:
https://votingtheory.org/archive/posts?where=%7B%22topic_id%22%3A566%7D
On Sun, Aug 11, 2024 at 8:22 AM Kristofer Munsterhjelm <
km-elmet@munsterhjelm.no> wrote:
On 2024-08-08 17:53, Closed Limelike Curves wrote:
I suspect the uncovered set might be slightly better because it's a
close approximation of the bipartisan set that isn't too hard to
explain. Maximal lotteries also have some very nice strategy-resistance
properties.
You've referred to the maximal lottery and strategic voting before. I'd
like to know in more detail what you're referring to by your statements.
In the Monroe post, you said:
If group strategy was a reasonable model of voters, it wouldn't
matter which electoral system we picked, because the outcome would
always be maximal lottery.
What do you mean? Do you mean that:
-
Every (non-strategyproof) method has a unique Nash equilibrium per
election under group strategy, whose expected outcome is that election's
maximal lottery, -
Every method has the maximal lottery as one of its Nash equilibria,
-
The relation between group strategy and the maximal lottery only holds
for some methods, and these methods have the ML as their unique Nash
equilibrium, -
As above, but "as one of its Nash equilibria".
or something else entirely?
On this topic and the lack of focus on proportional representation
mentioned elsewhere, I think it would be super useful to have some kind
of strongly-summable PR algorithm. ElectoWiki claims Ebert's method is
summable
<
https://electowiki.org/wiki/Summability_criterion#Multi-winner_generalizations_and_results>,
but the link is broken and Ebert has some big issues (e.g. negative
response and Pareto inefficiency).
I tried to look at the forum through IA and I couldn't find any mention
of strong summability; it must have been in a later post on that thread,
which IA hasn't archived. So at best that needs a {{cn}}.
To my knowledge, whether Droop proportionality is compatible with strong
summability is still open. I have a very broad idea of how one might
resolve summability questions like this, but I would need some
mathematical primitives that I'm not sure how to construct.
-km